1 Introduction

Since the beginning of the COVID-19 epidemic, policy makers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures and stay-at-home recommendations and including in addition the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.

The timing of the different interventions with respect to the spread of the contagion both at a global and intra-national level has been very different from country to country. This, in combination with demographical, economic, health-care related and area-specific factors, have resulted in different contagion patterns across the world.

Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.

different regions of Italy.

2 Data

The data used in this analysis refer to mainly two open datasets, i.e., the COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for contagion data (Dong, Du, and Gardner (2020)) and Oxford COVID-19 Government Response Tracker (OxCGRT) for policies tracking (Thomas et al. (2020)).

3 Containment strategies and resembling patterns

4 Effect of policies from a global perspective

Some countries have underestimated the dangerousness of the Coronavirus disease 2019 (COVID-19) and the importance to apply the containment measures. The little concern of some countries regarding the COVID-19 infectious disease is due by many and different reason. Some countries decided to save the economy instead of people lives, i.e., it is a method to fight a war, in this case the pandemic war. For that, we want to analyze which coutries adopt the ``optimal’’ policy measures to contain the contagion of COVID-19. Thanks to the Thomas et al. (2020) data sets, we know which type of measures each goverment take and when. The indicators of government response considered are \(17\) in total, that can be resumed in indicators of lockdown/social distancing, contact tracing, movement restrictions, testing policy, public health measures, and governance and socio-economic measures.

Therefore, some variables as the number of hospital beds are considered from OECD in order to have some additional covariates that can be influence the variation in government responses to COVID-19.

We restrict the wide range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.

The daily number of active person is analyzed as measure of COVID-19 situation. Being a count variable, we decide to use a Negative Binomial Regression in order to correct also for the possible overdispersion. Therefore, the hierarchical struture induced by the nested structure of countries inside the clusters and by the repeated measures statement. For that, we think to use a generalized mixed model with family negative binomial. The countries information as well as the clusters and date information are used as random effects in our model.

So, the aim is to understand how the lockdown policies influences the contagions. We consider the aligned data respect to the first confirmed case, we have the following situation:

Also, we lag the number of active respect to \(14\) days, in order to consider the influences of the restrictions imposed at time \(t\) on number of active at time \(t+14\), in order to make a correct impact. The observations are aligned respect to the first confirmed case across the countries, in order to have observations directly comparable in a longitudinal point of view.

4.1 Exploratory Analysis

The set of covariates considered in this analysis can be divided into three main area:

  1. Longitudinal economic variables;

  2. Longitudinal health system variables;

  3. Fixed demographic/economic/health variables.

4.1.1 Economic Variables

Name Measurement Description
Income Support Ordinal Government income support to people that lose their jobs
Debt/contract relief for households Ordinal Government policies imposed to freeze financial obligations
Fiscal measures USD Economic fiscal stimuli
International support USD monetary value spending to other countries

We will combine these two first economic variables into one continous variables using the Polychoric Principal Component Analysis, in order to diminuish the number of covariates inside the model, having \(9\) ordinal policies lockdown covariates.

Therefore, the two economic variables in USD are examined and transformed in logarithmic scale in order to de-emphasizes very large values.

For further details about the definition of the economic variables, please see the BSG Working Paper Series

4.1.2 Demographic/Fixed variables

We analyze various variables from the World Bank Open Data that are fixed along the temporal dimension:

Name Measurement
Population Numeric
Population ages 65 and above (% of total population) Numeric
Population density (people per sq. km of land area) Numeric
Hospital beds (per 1,000 people) Numeric
Death rate, crude (per 1,000 people) Numeric
GDP growth (annual %) Numeric
Urban population (% of total population) Numeric
Surface area (sq. km) Numeric

4.1.3 Health variables

We analyze two heatlh systems variables.

Name Measurement Description
Emergency Investment in healthcare USD Short-term spending on, e.g, hospitals, masks, etc
Investment in vaccines USD Announced public spending on vaccine development

Also in this case, we transform the set of healthy variables into one continous variable using the Polycorin Principal Component Analysis.

4.2 Model

The data are observed for each country nested within date. We are considering also the Clusters variable, therefore we have three level structure of the data. Therefore, the variability of the data comes from nested sources: countries are nested within clusters where the measures of the observations are repeated across time, i.e., longitudinal data.

For that, the mixed model approach is considered in order to exploit the different type of variability coming from the hierarchical structure of our data. Firstly, the Intraclass correlation coefficient (ICC) is computed:

\[ ICC_{date; active} = 0.0936 \quad ICC_{Countries; Active} = 0.4015 \quad ICC_{Clusters; Active} = 0.0951 \]

Therefore, the \(40.15\%\) of the variance of the data is given by the random effect of the countries, while the \(9.36\%\) by the temporal effect and \(9.51\%\) by the clusters effect. Therefore, the mixed model will impose of sure a random effect for the countries, the other two effects will be selected using the conditional AIC

The random effects are used to model multiple sources of variations and subject-specific effects, and thus avoid biased inference on the fixed effects. The dependent variable is the cumulated number of active person, therefore a count data model is considered. In order to control the overdispersion of our data, i.e., the conditional variance exceeds the conditional mean, the negative binomial regression with Gaussian-distributed random effects is used. Let \(n\) countries, and country \(i\) is measured at \(n_i\) time points \(t_{ij}\). The active person \(y_{ij}\) count at time \(t+14\), where \(i=1,\dots, n\) and \(j = 1, \dots,n_i\), follows the negative binomial distribution:

\[y_{ij} \sim NB(y_{ij}|\mu_{ij}, \theta) = \dfrac{\Gamma(y_{ij}+ \theta)}{\Gamma(\theta) y_{ij}!} \cdot \Big(\dfrac{\theta}{\mu_{ij} + \theta}\Big)^{\theta}\cdot \Big(\dfrac{\mu_{ij}}{\mu_{ij} + \theta}\Big)^{y_{ij}}\] where \(\theta\) is the dispersion parameter that controls the amount of overdispersion, and \(\mu_{ij}\) are the means. The means \(\mu_{ij}\) are related to the host variables via the logarithm link function:

\[\log(\mu_{ij}) = \log(T_{ij}) + X_{ij} \beta + Z_{ij} b_i \quad b_i \sim \mathcal{N}(0,\psi)\]

where \(\log(T_{ij})\) is the offset that corrects for the variation of the count of the active person at time \(t\). \(\text{E}(y_{ij}) = \mu\) and \(\text{Var}(y_{ij}) = \mu (1 + \mu\phi)\) from James W. Hardin (2018).

After some covariates selection steps and random effects selection, the final model is expressed as:

summary(mod1)
##  Family: nbinom2  ( log )
## Formula:          
## active_lag ~ pca_EC + pop_density_log + surface_area_log + pca_hs +  
##     workplace_closingF + gatherings_restrictionsF + transport_closingF +  
##     stay_home_restrictionsF + testing_policyF + contact_tracingF +  
##     Clusters + (0 + pca_LD | id) + (1 | date2) + (1 | Clusters)
## Data: dat
##  Offset: log(active + 1)
## 
##      AIC      BIC   logLik deviance df.resid 
##  40748.6  40921.6 -20344.3  40688.6     2330 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev. 
##  id       pca_LD      2.928e-01 5.411e-01
##  date2    (Intercept) 4.169e+00 2.042e+00
##  Clusters (Intercept) 4.215e-09 6.492e-05
## Number of obs: 2360, groups:  id, 20; date2, 158; Clusters, 5
## 
## Overdispersion parameter for nbinom2 family (): 1.07 
## 
## Conditional model:
##                           Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               -0.95466    0.70894  -1.347  0.17811    
## pca_EC                    -0.53735    0.07044  -7.629 2.37e-14 ***
## pop_density_log            0.15443    0.04620   3.342  0.00083 ***
## surface_area_log           0.05360    0.03587   1.494  0.13510    
## pca_hs                     0.05193    0.02029   2.559  0.01050 *  
## workplace_closingF1       -0.24604    0.14061  -1.750  0.08016 .  
## workplace_closingF2       -1.12441    0.14061  -7.997 1.28e-15 ***
## workplace_closingF3       -0.46986    0.17228  -2.727  0.00638 ** 
## gatherings_restrictionsF1 -0.52789    0.16317  -3.235  0.00122 ** 
## gatherings_restrictionsF2 -1.22558    0.14231  -8.612  < 2e-16 ***
## gatherings_restrictionsF3 -1.48631    0.17392  -8.546  < 2e-16 ***
## gatherings_restrictionsF4 -1.67393    0.17987  -9.306  < 2e-16 ***
## transport_closingF1       -0.04257    0.10635  -0.400  0.68897    
## transport_closingF2       -0.44643    0.20266  -2.203  0.02761 *  
## stay_home_restrictionsF1  -0.06059    0.10879  -0.557  0.57758    
## stay_home_restrictionsF2  -0.13755    0.14964  -0.919  0.35799    
## stay_home_restrictionsF3  -0.87098    0.29387  -2.964  0.00304 ** 
## testing_policyF1           0.20317    0.09147   2.221  0.02633 *  
## testing_policyF2           0.55401    0.11289   4.908 9.21e-07 ***
## testing_policyF3           1.30708    0.16002   8.168 3.13e-16 ***
## contact_tracingF1          0.20257    0.08292   2.443  0.01456 *  
## contact_tracingF2          0.37629    0.09576   3.929 8.51e-05 ***
## ClustersCl2                1.47291    0.17353   8.488  < 2e-16 ***
## ClustersCl3                1.93534    0.15847  12.213  < 2e-16 ***
## ClustersCl4                2.34541    0.14849  15.795  < 2e-16 ***
## ClustersCl5                2.43211    0.16041  15.162  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5 Italian lockdown and regional outcomes

6 Supplementary materials

All the codes used for this analysis is available on Github.

Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.

James W. Hardin, Joseph M. Hilbe. 2018. Generalized Linear Models and Extensions. 4th ed. Stata Press.

Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.